Question

8 to the power of 1/6 times by 2 to the power of x = 32 to the power of 1/2. Work out the value of x. ​

Answer 1

the exact value of x is 2

Explanation:

8⁽¹/⁶⁾ x 2ˣ = 32⁽¹/²⁾

32⁽¹/²⁾ = 2⁵⁽¹/²⁾ = 2⁽⁵/²⁾

8⁽¹/⁶⁾ = 2³⁽¹/⁶⁾ = 2⁽¹/²⁾

8⁽¹/⁶⁾ x 2ˣ = 2⁽¹/²⁾ x 2ˣ = 2⁽¹/²⁾+ˣ = 2⁽¹/²+ˣ⁾

since 8⁽¹/⁶⁾ x 2ˣ = 32⁽¹/²⁾ = 2⁽⁵/²⁾

2⁽¹/²+ˣ⁾ = 2⁽⁵/²⁾

equate the powers

1/2+ x = 5/2

subtract 1/2 from both sides

x = 5/2 - 1/2 = (5-1)/2 = 4/2 = 2

x = 2